I haven't even been able to free range my girls and so far there is a slight richer flavor to their eggs but I feed scratch and peck so they aren't getting any processed grain. I also have very sensitive taste buds so that could have something to do with it.
You may want to supplement that somehow, for nutrition sake, especially since you aren't able to free range.
I will say, I can taste the difference in my chicken and guinea eggs. I rarely eat eggs in general so I think that is why I can't taste the difference, since I can't even remember what a store bought egg tastes like our the last time I had one lol
From what I understand, the feed isn't processed food in the sense that, say, a bag of potato chips are. The grains are ground then fortified, a binder added, and then pelletized or left as crumble. I'd say it's similar to making a cake, bread, or pasta from scratch, which is still technically "processed" unless you are grinding your own flour, using raw sugar, and so on. There's nothing wrong with feeding whole grains either, but scratch grain mixtures are not formulated for complete nutrition at any life stage.